Location of a moving target with round trip time vectors using an airborne platform

ABSTRACT

A method and devices are disclosed that locate a target station moving at a constant velocity. A method and devices are disclosed for producing an RTT vector that is based upon the changes in position of the airborne measuring station position and the relative change in position of the target station. In one embodiment, the target station is an access point or station conforming to the IEEE 802.11 Standard and the airborne measuring station may also be a device that conforms to the IEEE 802.11 Standard.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to and claims priority to U.S. ProvisionalPatent Application Ser. No. 63/331,019, filed Apr. 14, 2022, entitledLOCATION OF A MOVING TARGET WITH ROUND TRIP TIME VECTORS USING ANAIRBORNE PLATFORM, the entirety of which is incorporated herein byreference.

TECHNICAL FIELD

The present disclosure relates to the geo-location of wireless devicesand in particular to a method and system for the geo-location ofwireless local area network (WLAN) devices.

BACKGROUND

Initially, it is noted that IEEE Standard 802.11-2020 is used as thebase reference for disclosures used in this disclosure, the entirecontents of which are incorporated herein by reference. The IEEE 802.11Standard is commonly referred to as “Wi-Fi”.

Determining the location of wireless devices can be performed by variousmethods. These methods may be classified as active, passive and combinedactive and passive. In an active location scheme, a device that isdetermining the location or range, “the measuring device”, transmitscertain packets to the device being located, “the target device”, andthe common method is to measure the time of arrival (TOA) of theresponse from the target device and compare that to the time ofdeparture (TOD) of the packet that was transmitted by the measuringdevice to determine the time for the round trip, RTT.

In such location systems it is common to use multiple measuring devicesto determine the location. In such a scheme, simultaneous TOA and/or TODmeasurements are taken by different measuring devices situated atdifferent points and the location of the target device calculated.

In an active location scheme, TOD may be measured for a packet that istransmitted from the measuring station addressed to the target station.The TOA of the response from the target station at the measuring stationis then also measured. If the turnaround time for the target station toreceive the packet from the measuring station and to start to transmitthe response is known, then the time difference at the measuring stationbetween the TOA and the TOD, minus the turnaround time at the targetstation will be directly proportional to twice the distance of thetarget station from the measuring station. For example, if the targetstation is a wireless device based upon IEEE 802.11 technology, and ifthe packet transmitted from the measuring station to the target stationis a data packet, the response from the target station will normally bean acknowledgement (ACK) packet. If the packet transmitted from themeasuring station to the target station is a control packet, for examplea request-to-send (RTS) packet, then the response from the targetstation will normally be a clear-to-send (CTS) packet. In these twoexamples, the turnaround time at the target station is defined in theIEEE 802.11 Standard as the short interframe spacing (SIFS), which is apreset value. Hence, the round trip time, RTT, between the measuringstation and the target station may be determined from the calculationRTT=(TOA−TOD−SIFS) and the distance between the measuring station andthe target station is then TDD*c/2, where c is the speed of light. Thismethod of estimating the distance to a target station by measuring theTOD and TOA and accounting for the turnaround time is known.

FIG. 1 is a diagram of a typical location system 100 which includesthree airborne measuring stations 110 a, 110 b and 110 c (referred tocollectively herein as “measuring stations” or “measuring receivers”).The target station 120 is a wireless device, for example an Access Point(AP) that is to be located by the three airborne measuring stations 110.The distance of the target station 120 from the airborne measuringstation 110 a is R1, 130. The distance of the target station 120 fromthe airborne measuring station 110 b is R2, 140. The distance of thetarget station 120 from the airborne measuring station 110 c is R3, 150.The round trip time, RTT1, determined from the calculationRTT=(TOA−TOD−SIFS), is measured for transmissions from the airbornemeasuring station 110 a and used to calculate the distance R1 130 usingthe formula R1=RTT1*c/2 where c is the speed of light. Similarly, RTT2and RTT3 measurements result in the determination of distances R2 140and R3 150. The methods for calculating the location of the targetstation 120 using the distances R1 130, R2 140 and R3 150 are wellknown.

In cases where there is a single airborne measuring station 110, as maybe the case when the station is airborne, then the three measuringdistances R1 130, R2 140 and R3 150 may be taken at different points intime. Time is required in order for the airborne measuring station 110to travel to the positions represented by 110 a, 110 b and 110 c asshown in FIG. 1 , to ensure angular intersections greater than 90degrees which would result in an acceptable geometrical dilution ofprecision GDOP. Over time, the location of the target station 120 can becalculated with increasing accuracy as more measurements are taken bythe airborne measuring station 110 from varying positions. Suchcalculations are well known, but there is a significant time delaybefore meaningful locations may result.

If, in order to obtain a faster location result, a directional antennamay be utilized at the single airborne measuring station 110, such thata direction may be known in addition to the distance to the targetcalculated from the RTT. FIG. 2 is a diagram of an airborne measuringstation 110 that is transmitting a ranging signal to a target station120. The range 210 of the target station 120 from the airborne measuringstation 110, R 210, may be estimated from the RTT. If a directionalantenna is deployed at the airborne measuring station 110, then theangle, Φ 220 of the direction of the received signal from the targetstation 120 can be measured. The location of the target station 120 canthen be estimated as being a distance of D 210 from the airbornemeasuring station 110 along a vector that is at an angle of Φ 220relative to the airborne measuring station 110. The accuracy of theestimated location will be dependent upon the directivity of the antennaat the airborne measuring station 110, and the accuracy of the RTTmeasurement.

The directivity of an antenna increases with the size and gain of theantenna. For example, an antenna with 5 degree beamwidth at 2.4 GHz mayhave dimensions in the order of 1.6 meters or 5.3 feet. Even with such adirectivity, if the airborne measuring station 110 is airborne at analtitude of 10,000 feet and at a ground distance of 3 miles, then theground location accuracy based solely upon the antenna angle of such avector based location, as described in FIG. 2 , would be in the order of±1400 feet.

In order to measure an accurate location of the target station 120 froman airborne measuring station 110 within a time period of seconds, thenthe use of a directional antenna requires an antenna of large dimensionswhich may be impractical for mounting on the airborne platform. Inaddition, a directional antenna may need to be controlled in elevationand azimuth so as to point in the direction of the target station 120resulting in complex circuitry and/or a gimballed antenna assembly.

Published U.S. Patent Application Nos. US2020/0158852 A1 andUS2020/0166630 A1 both disclose methods and devices for producing an RTTvector that is based upon the change in an airborne measuring stationposition and the corresponding RTT results taken at known time intervalsto a ground based target station. The disclosed methods can enable thelocation of a target station to a high accuracy within a period in theorder of seconds. In both cases the methods rely on the condition thatthe target station is in a fixed location. In the case of a movingtarget station, the methods may become inaccurate.

SUMMARY

Some embodiments provide to a method and system for the geo-location ofwireless local area network (WLAN) devices.

According to one aspect, a process in an airborne station fordetermining a location of a WD is provided. At each of a plurality ofpositions of the airborne station, at times t_(n-q) for q=0 to q, thefollowing are determined: the longitude X_(n-q) and latitude, Y_(n-q) ofthe airborne station; a round trip time RTT between the airborne stationand the WD; and a distance, Rn, of the WD from the airborne stationbased on the determined longitude, latitude and RTT. The airbornestation determines differences between earlier and later determinationsof the latitude and longitude and differences (ΔRTTs) between earlierand later determinations of RTT. The airborne station scales the RTTs toaccount for horizontal distance and altitude of the airborne station.The airborne station minimizes residuals between the determined ΔRTTsand a model ΔRTT, the model ΔRTT being based at least in part onparameters α, v_(N), and v_(E) of the model, a being an angle between Rnand a reference axis, v_(N) being a velocity of the WD in a firstdirection and v_(E) being a velocity of the WD in a second directionperpendicular to the first direction. The airborne station determines alocation of the WD based at least in part on a value for a thatminimizes the residuals and based at least in part on the distance Rn.

According to this aspect, in some embodiments, the model ΔRTT is basedat least in part on:

${{\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - q{para}}}{Rn}} \right)^{2} + \left( \frac{d_{n - q{perp}}}{Rn} \right)^{2}} - 1} \right\} 1}},$

where d_(n-q para)=COS(α)Δr_(N)+SIN(α) Δr_(E)+[COS(α) v_(N)+SIN(α)v_(E)]*(t_(n)−t_(n-q)); |d_(n-q perp)|=|−SIN(α) Δr_(N)+COS(α)Δr_(E)+[−SIN(α) v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q))|; and Δr_(N) is achange in latitude of the WD; Δr_(E) is a change in longitude of the WDand C is a speed of light. In some embodiments, values of v_(N) andv_(E) that minimize the residuals are used to predict an averagevelocity v=√{square root over (V_(N) ²+V_(E) ²)} of WD and a futurelocation of the WD. In some embodiments, the WD location is boxed byα±Δα, and by R±ΔR, where ΔR is related to an uncertainty in shortinterface spacing (SIFS) time and where α and Δα are derived from acorrelation matrix based on the model. In some embodiments,

${F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}};$

the RTTs are scaled by a factor given by where Alt_(n) is an altitude ofthe airborne station and R_(n) is the range in the same units as thealtitude. In some embodiments, the residuals are minimized based atleast in part on minimizing a sum of squared residuals. In someembodiments, the process further includes scaling the longitude X_(n-q)by COS (Y_(n-q)). In some embodiments, a measure of a final value of anRTT is based at least in part on an average of a number predeterminedRTTs. In some embodiments, Rn is determined based at least in part on adelay that is determined when the WD is stationary. In some embodiments,the residuals are based at least in part on a horizontal distancebetween the WD and the airborne station.

According to another aspect, an airborne station for determining alocation of a WD is provided. At each of a plurality of positions of theairborne station, at times t_(n-q) for q=0 to q, the following aredetermined by the processing circuitry of the airborne station: thelongitude X_(n-q) and latitude, Y_(n-q) of the airborne station; a roundtrip time RTT between the airborne station and the WD; and a distance,Rn, of the WD from the airborne station based on the determinedlongitude, latitude and RTT. The airborne station determines differencesbetween earlier and later determinations of the latitude and longitudeand differences (ΔRTTs) between earlier and later determinations of RTT.The airborne station scales the RTTs to account for horizontal distanceand altitude of the airborne station. The airborne station minimizesresiduals between the determined ΔRTTs and a model ΔRTT, the model ΔRTTbeing based at least in part on parameters α, v_(N) and v_(E) of themodel, a being an angle between Rn and a reference axis, v_(N) being avelocity of the WD in a first direction and v_(E) being a velocity ofthe WD in a second direction perpendicular to the first direction. Theairborne station determines a location of the WD based at least in parton a value for α that minimizes the residuals and based at least in parton the distance Rn.

According to this aspect, in some embodiments, the model ΔRTT is basedat least in part on:

${{\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - q{para}}}{Rn}} \right)^{2} + \left( \frac{d_{n - q{perp}}}{Rn} \right)^{2}} - 1} \right\} 1}},$

where d_(n-q para)=COS(α)Δr_(N)+SIN(α) Δr_(E)+[COS(α) v_(N)+SIN(α)v_(E)]*(t_(n)−t_(n-q)); |d_(n-q perp)|=|−SIN(α) Δr_(N)+COS(α)Δr_(E)+[−SIN(α) v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q))|; and Δr_(N) is achange in latitude of the WD; Δr_(E) is a change in longitude of the WDand C is a speed of light. In some embodiments, values of V_(N) andV_(E) that minimize the residuals are used to predict an averagevelocity v=√{square root over (v_(N) ²+v_(E) ²)} of WD and a futurelocation of the WD. In some embodiments, the WD location is boxed byα±Δα, and by R±ΔR, where ΔR is related to an uncertainty in shortinterface spacing (SIFS) time and where a and Act are derived from acorrelation matrix based on the model. In some embodiments, the RTTs arescaled by a factor given by

${F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}};$

where Alt_(n) is an altitude of the airborne station and R_(n) is therange in the same units as the altitude. In some embodiments, theresiduals are minimized based at least in part on minimizing a sum ofsquared residuals. In some embodiments, the airborne station is furtherconfigured to scale the longitude X_(n-q) by COS (Y_(n-q)). In someembodiments, a measure of a final value of an RTT is based at least inpart on an average of a number predetermined RTTs. In some embodiments,Rn is determined based at least in part on a delay that is determinedwhen the WD is stationary. In some embodiments, the residuals are basedat least in part on a horizontal distance between the WD and theairborne station.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present disclosure, and theattendant advantages and features thereof, will be more readilyunderstood by reference to the following detailed description whenconsidered in conjunction with the accompanying drawings wherein:

FIG. 1 is a diagram of a typical location system which includes threeairborne measuring stations;

FIG. 2 is a diagram of an airborne measuring station that istransmitting a ranging signal to a target station;

FIG. 3 is a timing diagram that describes a ranging transmission methodfor the measurement of RTTs from an airborne measuring station to atarget station;

FIG. 4 is a diagram of an example of an airborne measuring stationdepicted moving in a clockwise direction on a path, and a target stationmoving at a constant velocity vat an angle θ relative to the easterlydirection;

FIG. 5 is a vector diagram corresponding to FIG. 4 where v=0, i.e., thetarget station is stationary;

FIG. 6 is a vector diagram corresponding to FIG. 4 where the targetstation is moving at velocity v;

FIG. 7 is a vector diagram corresponding to FIG. 4 where the targetstation is moving at velocity vin direction θ;

FIG. 8 is a block diagram of an example measuring system that may beused in accordance with the principles described herein;

FIG. 9 is a flow diagram of an example of one embodiment of the processthat calculates the position of a moving mobile station; and

FIG. 10 is a flow diagram of another example process for determining theposition of a moving mobile station.

DETAILED DESCRIPTION

This Application incorporates U.S. Patent Application Publication Nos.2020/0158852 A1 and 2020/0166630 A1 by reference in their entirety.

Although this disclosure uses Wi-Fi as an example for the measurement ofthe round trip time (RTT), it should be clear to someone skilled in theart that the RTT measurement processes described herein can be measuredfor other wireless technologies and is thus not limited solely to Wi-Fi.Reference to a wireless device (WD) herein may therefore refer to awireless local area network (WLAN) device, although embodiments are notlimited to WLAN devices.

In one embodiment of the present disclosure, a single airborne measuringstation is used. A method and devices are disclosed that locate a targetstation moving at a constant velocity. A method and devices aredisclosed for producing an RTT vector that is based upon the changes inposition of the airborne measuring station position and the relativechange in position of the target station. In one embodiment, the targetstation is an access point or station conforming to the IEEE 802.11Standard and the airborne measuring station may also be a device thatconforms to the IEEE 802.11 Standard.

Returning to the drawing figures in which like reference numerals referto like elements, there is shown in FIG. 3 a timing diagram thatdescribes ranging a transmission method for the measurement of RTTs froman airborne measuring station 110 to a target station 120. Time axis 310is the time axis for the airborne measuring station 110 and time axis320 is the time axis for the target station 120. At time Ta 311, theairborne measuring station 110 starts the transmission of request packet350 which is addressed to the target station 120. Packet 350 may, forexample, be a data null or an RTS packet. After a time delay of td, attime Tb 321, the target station 120 starts to receive packet 350. Attime Tc 312, the airborne measuring station 110 completes thetransmission of packet 350 and at time Td 422, target station 120completes the reception of packet 350. The time difference between Tc412 and Td 422 is td 331, the propagation time for the packet to travelfrom the airborne measuring station 110 to the target station 120. Notethat the time differences (Tc−Ta) and (Td−Tb) are both the duration tp330 of the transmitted packet 350.

The target station 120 transmits the response packet 355 at time Te 323.The response packet 355 may be an ACK or an RTS packet in reply to thereceived request packet 350, time Te 323 ideally will be at a timet_(SIFS) 332 after time Td 322, where t_(SIFS) 332 is the SIFS time asdefined in the IEEE 802.11 Standard. In the general sense, individualstations may exhibit a variation, or delay, in the value of t_(SIFS)332. At time Tf 313, the airborne measuring station 110 starts toreceive the response packet 355. The time difference between Te 323 andTf 313 is td 333. At time Tg 324, the target station 120 completes thetransmission of the response packet 355 and at time Th 314, the airbornemeasuring station 110 completes receiving the response packet 355. Notethat the time differences (Tb−Ta), (Td−Tc), (Tf−Te) and (Th−Tg) are allequal and have the value td which is the propagation time for therequest packet and response packet to travel between the two stations.

At the airborne measuring station 110, the time recorded for a packetmay be taken at the end point of a frame where the frame check sum FCSframe has completed. Hence, the recorded time for the transmission ofrequest packet 350 is time Tc 312, and the time that is recorded for thereception of the response packet 355 is time Th 314. In order tocalculate the value of RTT, it is necessary to know the duration tr 334of the response packet 355. Calculating the duration tr 334 isstraightforward as the airborne measuring station 110 can monitordetails of the response packet such as data rate and length. In practicetherefore, the airborne measuring station 110 can calculate the value ofTOF from expression (1):

RTT=(Th−Tc−tc−t _(SIFS))  (1)

and hence, the corresponding distance, R=RTT×C/2  (2)

As mentioned previously, the packet exchange may be any pair of packetswhere an automatic response packet is sent. Commonly used Wi-Fi packetsinclude an RTS/CTS exchange and a Data (null)/ACK exchange.

FIG. 4 is a diagram of an example of an airborne measuring station 110depicted moving in a clockwise direction on a path 401, and a targetstation 120 moving at a constant velocity v at an angle θ 433 relativeto the easterly direction. At specific times, T, the target station 120may transmit a response packet 355. At time T_(n), the airbornemeasuring station 110 is at position (X_(n), Y_(n)) 410, and the targetstation 120 is at location (x_(n), y_(n)) 420. At time T_(n-1), theairborne measuring station 110 was at position (X_(n-2), Y_(n-1)) 411,and the target station 120 was at location (x_(n-1), y_(n-1)) 421. Attime T_(n-2), the airborne measuring station 110 was at position(X_(n-2), Y_(n-2)) 412, and the target station 120 was at location(x_(n-2), Y_(n-2)) 422. Note that, in this example, the airbornemeasuring station 110 is moving from position (X_(n-2), Y_(n-2)) 412, toposition (X_(n-1), Y_(n-1)) 411 to position (X_(n), Y_(n)) 410. Hence,position (X_(n), Y_(n)) 410 represents the latest position, and T_(n-2)is earlier than T_(n-1), and T_(n-1) is earlier than T_(n). At timeT_(n-2), the target station 120 was at location (x_(n-2), y_(n-2)) 422,and at time T_(n-1), the target station 120 was at location (x_(n-1),y_(n-1)) 421. The target station 120 is moving in a straight line at aconstant velocity v, angle θ 430. Therefore the distance betweenlocation (x_(n-2), y_(n-2)) 422 and (x_(n-1), y_(n-1)) 421 is vt_(n-1),where t_(n-1)=T_(n-2)−T_(n-1). Similarly, the distance between position(x_(n-1), y_(n-1)) 421 and (x_(n), y_(n)) 420 is vt_(n), wheret_(n)=T_(n-1)−T_(n).

At time T_(n), when the airborne measuring station 110 is at position(X_(n), Y_(n)) 410, the distance to the target station 120 is R_(n) 430and R_(n) 430 is at an angle α 440 where:

cos α=(Y _(n) −y _(n))/R _(n) and sin α=(x _(n) −x _(n))/R _(n)

At time T_(n-1), when the airborne measuring station 110 is at position(X_(n-1), Y_(n-1)) 411, the distance to the target station 120 isR_(n-1) 431, and at time T_(n-2), when the airborne measuring station110 is at position (X_(n-2), Y_(n-2)) 412, the distance to the targetstation 120 is R_(n-2) 432.

For q=1 to q, the distance r_(n-q) between positions (X_(n-q), Y_(n-q))and (X_(n), Y_(n)), is:

r _(n-q)=√{square root over ((x _(n) −X _(n-q))²+(Y _(n) −Y_(n-2))²)}  (3)

The distance r_(n-2) between positions (X_(n-2), Y_(n-2)) 411 and(X_(n), Y_(n)) 410, is:

r _(n-2)=√{square root over ((x _(n) −X _(n-2))²+(Y _(n) —Y _(n-2))²)}

where r_(n-1) is at an angle Ø_(n-1) 435, and where

$\begin{matrix}{{{\cos\phi_{n - 1}} = {{\left( {X_{n} - X_{n - 1}} \right)/r_{n - 1}{and}\sin\phi_{n - 1}} = {\left( {Y_{n - 1} - Y_{n}} \right)/r_{n - 1}}}}{{Hence},{\phi_{n - q} = {A{{COS}\left( \frac{\left( {X_{n} - X_{n - q}} \right)}{r_{n - q}} \right)}}}}} & (4)\end{matrix}$ $\begin{matrix}{{{And}{r_{n - q}(t)}{COS}\phi_{n - q}} = {\left( {X_{n} - X_{n - q}} \right) = {\Delta X_{n - q}}}} & (5)\end{matrix}$ $\begin{matrix}{{{r_{n - q}(t)}{SIN}\phi_{n - q}} = {{- \left( {Y_{n} - Y_{n - q}} \right)} = {{- \Delta}Y_{n - q}}}} & (6)\end{matrix}$

The target station 120 is moving at angle θ 433 at a velocity of v.Hence, the distance travelled is vt, where t is time between readings:

vt _(n-q) COS θ=x _(n) −X _(n-q) =Δx _(n-q)  (7)

vt _(n-q) SIN θ=y _(n) −Y _(n-q) =Δy _(n-q)  (8)

FIG. 5 is a vector diagram corresponding to FIG. 4 where v=0, i.e., thetarget station 120 is stationary. Rn 510 extends between points D 501and E 502 and makes an angle α 440 with respect to a reference axis.Vector r(t)_(n-q) 520, the change of position of the airborne measuringstation 110, is between points E 502 and F 503. Vector R_(n-q) (stat)512 is the sum of vectors R_(n) 510 and −r(t)_(n-q) 520, and is betweenpoints D 501 and F 503:

R _(n-q)(stat)=R _(n) +r(t)_(n-q)  (9)

Vector r(t)_(n-q) 520 is at an angle Ø_(n-q) 531 as discussed above withreference to equations (4), (5) and (6).

Define d _(n-q)(stat)=r(t)_(n-q)

and define unit vector u: u=R _(n) /R _(n)

Then: d _(n-q para)(stat)=d _(n-q)(stat)·u

And: d _(n-q perp)(stat)=|d _(n-q)(stat)×u|

With reference to FIG. 5 , d_(n-q para) (stat) 522 is between points E502 and G 504, and d_(n-q perp) (stat) 524 is between points G 504 and F503. In triangle EFG, angle ∠EFG 532 is (Ø_(n-q)−α), hence:

d _(n-q para)(stat)=r _(n-q)(t)SIN(Ø_(n-q)−α)  (10)

and: d _(n-q perp)(stat)=r _(n-q)(t)COS(Ø_(n-q)−α)  (11)

Hence, R_(n-q) (stat) 512 is:

R ² _(n-q)(stat)=[Rn+d _(n-q para)(stat)]² +d ² _(n-q perp)(stat)

And: ΔR _(n-q)(Stat)=R _(n-q)(Stat)−R _(n)

ΔR _(n-q)(stat)=√{square root over ((R _(n) +d _(n-q)(stat))² +d ²_(n-q perp)(stat)−R _(n))}  (12)

FIG. 6 is a vector diagram corresponding to FIG. 4 where the targetstation 120 is moving at velocity v from location M 640 to location D501. Vector r(t)_(n-q) 520, the change of position of the airbornemeasuring station 110 is between points E 502 and F 503. Vector Rn 510is the vector from the airborne measuring station 110 at location E 502,the current location of the airborne measuring station 110, to thetarget station 120 at location D 501, the current location of the targetstation 120. Vector r(t)_(n-q) 520 is the change of position of theairborne measuring station 110, which moves from location F 503, aprevious location, to location E 502. Vector vt_(n-q) 620 represents thedisplacement of the target station 120 from location M 640, at a timecorresponding to when the airborne measuring station was at location F503, to location D 501, at a time corresponding to when the airbornemeasuring station 110 is at location E 502. R_(n-q) 612 is a vector fromthe airborne measuring station 110 when at location F 503 to the targetstation 120 at location M 640.

A more complete understanding of the present disclosure, and theattendant advantages and features thereof, will be more readilyunderstood by reference first to a vector analysis of the relationshipof various vectors and components, followed by a detailed trigonometricanalysis.

Each time, T_(n-q), that the target station 120 sends a response packet355 after having received a request packet 350 from the airbornemeasuring station 110, there is an opportunity to determine absolutedistances. more importantly, the changes in RTT, ΔRTT, may be used todetermine directions and velocities without need of knowing the value ofthe SIFS time t_(SIFS) 332. Hence, ΔRTTq can be associated with a changein distance where:

change-in-distance=c*ΔRTTq/2=Rn-q−R _(n)

With reference to FIG. 6 , distances R_(n-q) and Rn are related to themagnitudes of the corresponding vectors Rn-q 612 and Rn 510:

Rn-q−Rn=|Rn-q|−|Rn|

With reference again to FIG. 6 : Rn-q=−r(t)_(n-q)+Rn−v(t_(n)−t_(n-q)).

Define: d _(n-q) =−r(t)_(n-q) −v(t _(n) −t _(n-q)).

then: d _(n-q para) =d _(n-q) ·u

and: d _(n-q perp) =|d _(n-q) ×u|

Then the differences in RTT measurements, ΔRTT, between an earlier time,t_(n-q), and the current time, t_(n), is:

$\begin{matrix}{\begin{matrix}{{\left( {c/2} \right)*\Delta{RTT}} = {{{Rn} - q - {Rn}} = {{❘{{- {r(t)}_{n - q}} + {Rn} - {vt}_{n - q}}❘} - {❘{Rn}❘}}}} \\{= {{❘{{Rn} + d_{n - q}}❘} - {❘{Rn}❘}}} \\{= {\sqrt{\left( {{Rn} + d_{n - q}} \right) \cdot \left( {{Rn} + d_{n - q}} \right)} - {Rn}}} \\{= {\sqrt{\left( {{Rn}^{2} + d_{n - q}^{2} + {2{{Rn} \cdot d_{n - q}}}} \right)} - {Rn}}} \\{= {\sqrt{{Rn}^{2} + d_{n - {q{para}}}^{2} + d_{n - {q{perp}}}^{2} + {2{Rn}*d_{n - {q{para}}}}} - {Rn}}} \\{= {\sqrt{\left( {{Rn} + d_{n - {q{para}}}} \right)^{2} + d_{n - {q{perp}}}^{2}} - {Rn}}}\end{matrix}{{Then}:}\begin{matrix}{{\Delta{RTT}} = {\left( {2/c} \right)*\left( {{Rn} - q - {Rn}} \right)}} \\{= {\left( {2/c} \right)*{Rn}*\left\{ {\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{Rn}} \right)^{2} + \left( \frac{d_{n - {q{perp}}}}{Rn} \right)^{2}} - 1} \right\}}}\end{matrix}} & (13)\end{matrix}$

Equation (13) has two unknowns, d_(n-q para) and d_(n-q perp). Rn may becalculated from the final RTT measurement at time Tn. The parameters ofinterest are the angle α 440 of Rn 510 relative to north (azimuth totarget) and the components of the velocity v of the target station 120relative to the geographic coordinate system, v_(N) and v_(E). Theunknowns d_(n-q para) and d_(n-q perp) may be written in known termsΔr_(N) and Δr_(E) and unknown variables v_(N) and v_(E) using the unitvector u=Rn/Rn:

u=Rn/Rn=COS(α)Ň+SIN(α){hacek over (E)}

Δr _(N) =Ň·r(t)_(n-q) ,Δr _(E) ={hacek over (E)}·r(t)_(n-q)

v _(N) =Ň·v,v _(E) ={hacek over (E)}·v

where Ň is the unit vector in the north direction and {hacek over (E)}is the unit vector in the east direction. Hence,

$\begin{matrix}\begin{matrix}{{- d_{n - {q{para}}}} = {{- u} \cdot d_{n - q}}} \\{= {{{{COS}(\alpha)}{\overset{\bigvee}{N} \cdot {r(t)}_{n - q}}} + {{{SIN}(\alpha)}{\overset{\smile}{E} \cdot {r(t)}_{n - q}}} +}} \\{\left\lbrack {{{{COS}(\alpha)}{\overset{\bigvee}{N} \cdot v}} + {{{SIN}(\alpha)}{\overset{\smile}{E} \cdot v}}} \right\rbrack*\left( {t_{n} - t_{n - q}} \right)} \\{= {{{{COS}(\alpha)}\Delta r_{N}} + {{{SIN}(\alpha)}\Delta r_{E}} +}} \\{\left\lbrack {{{{COS}(\alpha)}v_{N}} + {{{SIN}(\alpha)}v_{E}}} \right\rbrack*\left( {t_{n} - t_{n - q}} \right)}\end{matrix} & (14)\end{matrix}$ $\begin{matrix}{{And}:\begin{matrix}{{- d_{n - {q{perp}}}} = {- {❘{u \times d_{n - q}}❘}}} \\{= {❘{{{- {{SIN}(\alpha)}}{\overset{\bigvee}{N} \cdot {r(t)}_{n - q}}} + {{{COS}(\alpha)}{\overset{\smile}{E} \cdot {r(t)}_{n - q}}} +}}} \\{{\left\lbrack {{{- {{SIN}(\alpha)}}{\overset{\bigvee}{N} \cdot v}} + {{{COS}(\alpha)}{\overset{\smile}{E} \cdot v}}} \right\rbrack*\left( {t_{n} - t_{n - q}} \right)}❘} \\{= {❘{{{- {{SIN}(\alpha)}}\Delta r_{N}} + {{{COS}(\alpha)}\Delta r_{E}} +}}} \\{{\left\lbrack {{{- {{SIN}(\alpha)}}v_{N}} + {{{COS}(\alpha)}v_{E}}} \right\rbrack*\left( {t_{n} - t_{n - q}} \right)}❘}\end{matrix}} & (15)\end{matrix}$

Where the 2D relation |A×B|=|−A_(y)B_(x)+A_(x)B_(y)| has been used.Referring again to FIG. 5 , the term [COS(α) Δr_(N)+SIN(α) Δr_(E)] inequation (14) is d_(n-q para) (stat) 522 and the term [−SIN(α)Δr_(N)+COS(α) Δr_(E)] is d_(n-q perp) (stat) 524. The remaining terms inequations (14) and (15) refer to the movement of the target station 120and hence, referring again to FIG. 6 , the term [COS(α) v_(N)+SIN(α)v_(E)]*(t_(n)−t_(n-q)) in equation (14) is d_(n-q para) (mov) 622 andthe term [−SIN(α) v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q)) in equation (15)is d_(n-q perp) (mov) 624.

In equations (14) and (15), the only unknown quantities are α 440 and v(or equivalently the north component v_(N) and the east componentv_(E)). The quantity r(t)_(n-q) (Δr_(N), Δr_(E)) is the known differencein the airborne measuring station 110 locations, F 503 and E 502 whichmay be determined, for example, from a GPS module 860 on the airbornemeasuring station 110 as discussed below with reference to FIG. 8 .

In one embodiment of this disclosure, the method for determining theangle of arrival a 440, and the components of target velocity v_(N) andv_(E) is to measure the ΔRTT for 30 to 90 seconds (as required togenerate statistics) and vary the parameters α, v_(N), and v_(E) inequations (14) and (15) substituted into equation (13) until a best fitto the data is obtained as discussed below with reference to step 911 inFIG. 9 . If the airborne measuring station 110 is at a differentaltitude compared to the target station 120 at ground level, then alldistances obtained from RTTs may be projected to the ground level byfactor F which may be accomplished by taking the square root of the sumof the distance squared minus the altitude squared, in the same units,i.e.,

$F = {\frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}.}$

FIG. 7 is a vector diagram corresponding to FIG. 4 where the targetstation 120 is moving at velocity v in direction θ 430. Rn 510 is at anangle of α 440 between points D 501 and E 502. Vector r(t)_(n-q) 520,the change of position of the airborne measuring station 110, is betweenpoints E 502 and F 503. Note that vector vt_(n-q) 620 is between pointsF 503 and H 710. It should be noted that the vector vt_(n-q) is the samevector as vt_(n-q) 620 in FIG. 6 , but is drawn from point F 503, whichis in accordance with the cumulative law for addition of vectors. VectorR_(n-q) (mov) 612 is the sum of vectors R_(n), r(t)_(n-q), and vt_(n-q),and is between points D 501 and H 610:

R _(n-q)(mov)=R _(n) +r(t)_(n-q) +vt _(n-q)  (16)

Vector vt_(n-q) 620 is at an angle θ 430 as discussed above withreference to equations (7) and (8).

Define d _(n-q)(mov)=Vt _(n-q)

then d _(n-q para)(mov)=d _(n-q)(mov)·u

and d _(n-q perp)(mov)=|d _(n-q)(mov)×u|

With reference to FIG. 7 , d_(n-q para) (mov) 622 is between points H710 and K 714, and also between points J 713 and G 504. Also withreference to FIG. 7 , d_(n-q perp) (mov) 624 is between points F 503 andK714.In triangle HFK, angle ∠HFK is (θ+α), hence,

d _(n-q para)(mov)=vt SIN(θ+α)  (17)

and: d _(n-q perp)(mov)=vt COS(θ+α)  (18)

From FIG. 7 triangle DHJ, and equation (16), d_(n-q para) 732 andd_(n-q perp) 730, are:

d _(n-q para) =d _(n-q para)(stat)+d _(n-q para)(mov)  (19)

d _(n-q perp) =d _(n-q perp)(stat)−d _(n-q perp)(mov)  (20)

And R ² _(n-q)(mov)=[Rn+d _(n-q para)]² +d ² _(n-q perp)

Hence, Δ_(Rn-q)(mov)=√{square root over ((R _(n) +d _(n-q para))² +d ²_(n-q perp) −R _(n))}  (21)

Substituting equations (10) and (16), into equation (19):

d _(n-q para) =r _(n-q)(t)SIN(Φ_(n-q)−α)+vt SIN(θ+α)

Expanding the SIN terms:

d _(n-q para) =r _(n-q)(t)(SIN Φ_(n-q) COS α−COS Φ_(n-q) SIN α)+vt(SIN θCOS α+COS θ SIN α)

Substituting equations (5), (6), (7) and (8):

d _(n-q para) =−ΔY _(n-q) COS α−ΔX _(n-q) SIN α+Δy _(n-q) COS α+Δx_(n-q) SIN α  (22)

Substituting equations (11) and (17), into equation (20):

d _(n-q perp) =r _(n-q)(t)COS(Φ_(n-q)−α)−vt COS(θ+α)

Expanding the COS terms:

d _(n-q perp) =r _(n-q)(t)(COS Φ_(n-q) COS α−SIN Φ_(n-q) SIN α)−vt(COS θCOS α−SIN θ SIN α)

Substituting equations (5), (6), (7) and (8):

d _(n-q perp) =ΔY _(n-q) SIN α−ΔX _(n-q) COS α+Δy _(n-q) SIN α−Δx _(n-q)COS α  (23)

From equation (21), dividing and multiplying by R_(n) shows the changein RTT, ΔRTT:

$\begin{matrix}{{\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{Rn}} \right)^{2} + \left( \frac{d_{n - {q{perp}}}}{Rn} \right)^{2}} - 1} \right\}}} & (24)\end{matrix}$

It may be noted that equation (24) is the same as equation (13).

In equations (22) and (23), ΔY_(n-q) and ΔX_(n-q) are the differences inlongitude and latitude, respectively, of the airborne measuring station110 between the time t_(n) of the last measurement of R_(n) and the timet_(n-q) when R_(n-q) was measured. Note that ΔY_(n-q), may be correctedfor higher latitudes.

In equations (22) and (23):

Δy _(n-q) =v _(N)(t _(n) −t _(n-q)),  (25)

where v_(N) is the velocity of the target station 120 in the northerlydirection.

And: Δx _(n-q) =v _(E)(t _(n) −t _(n-q)),  (26)

where v_(E) is the velocity of the target station 120 in the easterlydirection.

Hence, the equation (24) with substitutions for d_(n-q para) andd_(n-q perp) from equations (22) and (23), and then v_(N) and v_(E) fromequations (25) and (26) describe the measurement ΔRTT in terms of threeparameters, a, v_(N), and v_(E) and two variables, ΔY_(n-q) andΔX_(n-q).

Hence, in summary:

$\begin{matrix}{{\Delta{RTT}} = {{\left( \frac{2R_{n}}{C} \right)\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{R_{n}}} \right)^{2} + \frac{d_{n - {q{perp}}}^{2}}{R_{n}}}} - 1}} & (24)\end{matrix}$

where

d _(n-q para) =−ΔY _(n-q) COS α—ΔX _(n-q) SIN α+v _(N)(t _(n) −t_(n-q))COS α+v _(E)(t _(n) −t _(n-q))SIN α  (27)

And

d _(n-q perp) =ΔY _(n-q) SIN α−ΔX _(n-q) COS α+v _(N)(t _(n) −t_(n-q))SIN α−v _(E)(t _(n) −t _(n-q))COS α  (28)

There is a third variable, the altitude of the airborne measuringstation 110, but this may be used to scale the ΔRTT to a horizontalcomponent. The RTT measurements may be multiplied by a factor F toaccount for the ratio of the horizontal distance R_(H) from the airbornemeasuring station 110 and the target station 120. Hence, R_(Hq)=RTT. F,where

$F = {\frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}.}$

It may be assumed that the altitude does not change significantly overthe time of the measurements, and hence, to simplify the procedure, onlythe final RTT may be used for the correction. Alternatively, each RTTmeasurement could be factored. Also the longitude measurement X_(n-q)may be scaled by a factor to account for reduced distance per degreewhen not at the equator.

Hence, X′ _(n-q) =X _(n-q)·COS(X _(n)).

The fitting parameters α, v_(N), and v_(E) as defined in equations (24),(27) and (28) may be varied to minimize the sum of the least squaredifferences for the measured ΔRTT with time, resulting from the RTTmeasurements as described above with reference to FIGS. 1, 2 and 3 , andthe calculated ΔR_(n-q) (mov) as per equation (18) for q=1 to q.

FIG. 8 is a block diagram of an example measuring system 800 that may beused in accordance with the principles described herein. In oneembodiment, measuring system 800 may be the airborne measuring station110. In one embodiment, measuring system 800 may include an antennaassembly 880, a transmitter receiver 810, a computer system 830, aglobal positioning system (GPS) module 840, a gyro module 860 and anetwork switch 850 such as an Ethernet switch.

The transmitter receiver 810 may transmit or receive radio frequency(RF) signals to and from the antenna assembly 880. The GPS module 840output may be connected to the transmitter receiver 810. The GPS module840 may provide the latitude, longitude and altitude of the airborneplatform of the measuring system 800. The transmitter receiver 810 mayappend GPS information to any RF transmission and/or reception. Thenetwork switch 850 may be connected to the Transmitter Receiver 810 andthe computer system 830. The transmitter receiver 810 may include an RFtransmitter 811, an RF receiver 812 and processing circuitry 815. The RFreceiver 812 may receive RF signals from the antenna assembly 880. TheRF receiver 812 may comprise one or more receiver paths. The RF receiver812 may perform the usual functions of an RF receiver such as low noiseamplification, filtering, and frequency down conversion so as tocondition the received signal suitable for inputting to the processingcircuitry 815. The processing circuitry 815 may perform the usualbaseband functions such as demodulation, descrambling, and errorcorrection of received packets as described in the I.E.E.E. 802.11Standard. The RF transmitter 811 may comprise one or more transmitterpaths. The RF transmitter 811 may perform the usual function of an RFtransmitter such as up conversion, filtering and power amplification ofthe baseband signal received from the processing circuitry 815 fortransmission via the antenna assembly 880. The processing circuitry 815may perform the usual baseband functions such as coding, scrambling andmodulation of packets to be transmitted as described in theabove-referenced I.E.E.E. 802.11 Standard. The processing circuitry 815may comprise a processor 816 and a memory 817. The processing circuitry815 may be configured to control any of the methods and/or processesdescribed herein and/or to cause such methods, and/or processes to beperformed, e.g., by the transmitter receiver 810. The memory module 817is configured to store data, programmatic software code and/or otherinformation described herein. In some embodiments, the software mayinclude instructions that, when executed by the processing circuitry815, causes the processing circuitry 815 to perform the processesdescribed herein with respect to the transmitter receiver 810.

According to this embodiment of the disclosure, the transmitter receiver810 may be configured to measure and monitor an input signal'sattribute, such as may include one or more of a ranging signaltransmitted by RF transmitter 811, data and control packets, and theresponse signal, including control packets, transmitted by an accesspoint or station that may be based upon the I.E.E.E. 802.11 Standard, asdiscussed above with reference to FIG. 3 . Such packets may include datanull, ACK, RTS and CTS packets. The memory 817 may store instructionsfor executing any method mentioned in the I.E.E.E. 802.11 Standard,input signals, and results of processing of the processor 816, signalsto be outputted and the like.

According to an embodiment of the disclosure, the RF transmitter 811 maybe configured to transmit signals and the processing circuitry 815 maybe configured to prepare the transmitted signal attributes based uponthe I.E.E.E. 802.11 Standard. Such transmitted packets may include datapackets, control packets and management packets that are to betransmitted by a wireless station that is based upon the I.E.E.E. 802.11Standard. Such data packets may include data null packets. Such controlpackets may include RTS packets. The memory 817 may store instructionsfor executing any method mentioned in the specification, input signals,and results of processing of the processor 816, signals to be outputtedand the like.

According to another embodiment of the disclosure, the transmitterreceiver 810 may be configured to receive the transmissions of anothertarget station 120 and the processing circuitry 815 may be configured tomonitor an attribute of the transmissions of the other target station120, and determine the value of the time of arrival of packets from theother target station 120, as discussed above with reference to FIG. 3 .In addition, according to an embodiment of the disclosure, thetransmitter receiver 810 may be configured to measure the times ofdeparture of the transmissions from the RF transmitter 811.

The GPS information may be provided to the processing circuitry 815 bythe GPS module 840. RF receptions may have the GPS information addedsuch that the position of the airborne platform 110 is known for eachreceived signal. The transmitter receiver 810 may include more than oneradio and therefore any transmission may be automatically received byanother radio within the transmitter receiver and by this means, theairborne platform position 110 is also known for each transmission. TheGPS information may be sent to the network switch 850 and therefore madeavailable to the computer system 830.

The computer system 830 may include an interface 831. Interface 831 maycontain an Ethernet connection to the network switch 850, the connectionto a display 836, a connection to a keyboard and mouse 837 as well asinterfacing to the processing circuitry 835. In some embodiments, theprocessing circuitry 835 may include a processor 832, a memory 833 and adatabase 834. The database 834 may contain the ground mappinginformation of the area of interest and the processor 832 and memory 833may be used to carry out the example processes described below withreference to FIG. 9 , using information on the position of the airborneplatform derived from the GPS module 840, the gyro module 860, andinformation on the target station 120 which may be inputted using thekeyboard and mouse 837. The display 836 may be used to show the groundmap together with the estimated location(s) of the target station 120.Note that the modules discussed herein may be implemented in hardware ora combination of hardware and software. For example, the modules may beimplemented by a processor executing software instructions or byapplication specific integrated circuitry configured to implement thefunctions attributable to the modules. Also note that the term“connected to” as used herein refers to “being in communication with”and is not intended to mean a physical connection nor a directconnection. It is contemplated that the signal path between one elementand another may traverse multiple physical devices.

Thus, in some embodiments, the processing circuitry 835 may include thememory 833 and a processor 832, the memory 833 containing instructionswhich, when executed by the processor 832, configure the processor 832to perform the one or more functions described herein. In addition to atraditional processor and memory, the processing circuitry 835 maycomprise integrated circuitry for processing and/or control, e.g., oneor more processors and/or processor cores and/or FPGAs (FieldProgrammable Gate Array) and/or ASICs (Application Specific IntegratedCircuitry).

The processing circuitry 835 may include and/or be connected to and/orbe configured for accessing (e.g., writing to and/or reading from) thememory 833, which may include any kind of volatile and/or non-volatilememory, e.g., cache and/or buffer memory and/or RAM (Random AccessMemory) and/or ROM (Read-Only Memory) and/or optical memory and/or EPROM(Erasable Programmable Read-Only Memory). Such memory 833 may beconfigured to store code executable by control circuitry and/or otherdata, e.g., data pertaining to communication, e.g., configuration and/oraddress data of nodes, etc. The processing circuitry 835 may beconfigured to control any of the methods described herein and/or tocause such methods to be performed, e.g., by the processor 832.Corresponding instructions may be stored in the memory 833, which may bereadable and/or readably connected to the processing circuitry 835. Inother words, the processing circuitry 835 may include a controller,which may comprise a microprocessor and/or microcontroller and/or FPGA(Field-Programmable Gate Array) device and/or ASIC (Application SpecificIntegrated Circuit) device. It may be considered that the processingcircuitry 835 includes or may be connected or connectable to memory,which may be configured to be accessible for reading and/or writing bythe controller and/or processing circuitry 835.

FIG. 9 is a flow diagram of an example of one embodiment of the process900 that calculates the position of a moving mobile target STA 120.Process 900 may start at step 901 where the final location, latitude_(n)and longitude_(n), of the airborne measuring station 110, and the finalRTT measurement, RTT_(n) are determined. For example, with reference toFIG. 4 , the final location of the airborne measuring station 110 isposition 410, latitude Y_(n), and longitude X_(n), and the correspondingRTT measurement, RTT_(n), is related to R_(n) 430, where RTT_(n)=2R_(n)/C. The final measurement of the latitude and longitude and RTT ofthe airborne measuring station 110 may also be determined over anaverage of a number of measurements in order to remove RTT fluctuations.For example, the average may be taken for the final 5 measurements. Thelatitude and longitude measurements may be derived from the GPS 840and/or the gyro module 860. The RTT may be measured by transmitting, viaRF transmitter 811, a request packet 350 and receiving, via RF receiver812, the response packet 355, as discussed above with reference to FIG.3 . The measurement may be carried out in processor 816 and stored inmemory 817. The results of the measurements may be inputted to theprocessing circuitry 835, via Ethernet switch 850, and stored indatabase 834.

In step 903, the differences between earlier measurements of thelatitude, longitude RTT and RTT may be derived, together with the timesof the measurements, t_(q). Hence, for q=1 to q:

latitude_(q)=latitude_(n-q)−latitude_(n) or Y _(q) =Y _(n-q) −Y _(n)

longitude_(q)=longitude_(n-q)−longitude_(n) or X _(q) =X _(n-q) −X _(n)

RTT_(q)=RTT_(n-q)−RTT_(n)

t _(q) =t _(n-q) −t _(n)

These calculations may be carried out in the processing circuitry 815and/or processing circuitry 835 and the results stored in memory 833 andor database 834.

In step 905, as discussed above with reference to equations (24), (27)and (28), the RTT measurements may be multiplied by a factor F toaccount for the ratio of the horizontal distance R_(H) from the airbornemeasuring station 110 and the target station 120.

Hence, R _(Hq)=RTT_(q) ·F, where

$F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}$

It may be assumed that the altitude does not change significantly overthe time of the measurements, and hence, to simplify the procedure, onlythe final RTT is used for the correction factor F. Alternatively, eachRTT measurement could be multiplied by factor F

In step 907 the longitude measurement X_(q) may be scaled by a factor toaccount for reduced distance per degree when not at the equator.

Hence, X′ _(q) =X _(q)·COS(X _(n))

Note that the units of R_(Hq), may be converted to microseconds, theunits of X_(q) and Y_(q) to meters, and the units of time to secondssuch that the speed of light C=300 m/μs, the target station 120 constantvelocity v will be in m/s, and the distance r_(n-q) between positions(X_(n-q), Y_(n-q)) and (X_(n), Y_(n)), will be in meters.

In step 909 the value for Rn is determined. As discussed above withreference to FIG. 3 and equations (1) and (2), the value for R may beexpressed as R=(TOA−TOD−packet length−(SIFS+delay))×C/2 where the onlyunknown is the “delay” which is the variation in SIFS time for anyparticular target station 120. A value for this delay, i.e., theeffective SIFS, may have be determined by previous location calculationswhen the target station 120 was stationary. However, observation ofequations (13) and (24) indicates that ΔRTT is not that sensitive toabsolute R and a deviation of perhaps 10% is not critical,

In step 911 a minimization of the summation of squared residuals, SSR,fitting process, such as Levenberg-Marquardt may be used to determinethe parameters α, v_(N) and v_(E) that minimize the residual,(R_(H)−ΔRTT)² where ΔRTT is given by equations (24), (27) and (28).Alternatively, the minimization of the SSR fitting process may use the“Pass Filter” function as described in U.S. Patent ApplicationPublication No: US 2021/0302566.

In step 913, for a final location, i.e., latitudes and longitudes, ofthe airborne measuring station 110, and the final RTT measurement,RTT_(n), step 911 may be repeated using varying time spans in the past.For example, data from time spans of 30 to 90 seconds in the past may beused until there is sufficient data such that the correlation matrixused in the fitting process indicates a sufficiently small uncertaintyin α 440, for example, ±5 degrees or 1/10 radians. The target stationvelocities, v_(N) and v_(E) are included in the fitting process in orderto get a valid value for angle α 440 and the corresponding targetstation 120 velocity, v, where v=√{square root over (v_(N) ²+v_(E) ²)}may be used to predict a future location of the target station 120.

In step 915 the uncertainties in a and R are determined. The targetstation 120 location may be boxed by α±Δα, and by R±ΔR, where ΔR isrelated to the uncertainty in SIFS time as discussed above in step 907,i.e., “delay”×C. Here, α and Δα may be derived from the correlationmatrix of a successful fitting process as discussed above with respectto step 913.

In step 917, consistency checks may be performed with previousmeasurements in order to gain confidence that the assumption of themodel, i.e., that the effect of the target station 120 velocity overtime can be replaced by an average velocity, is valid.

FIG. 10 is a flowchart 1000 of an example process in an airborne station110, performed by processing circuitry 835 for determining a location ofa WD. In step 1001, at each of a plurality of positions of the airbornestation, at times t_(n-q) for q=0 to q, the following are determined:the longitude X_(n-q) and latitude, Y_(n-q) of the airborne station(Step 1003); a round trip time RTT between the airborne station and theWD (Step 1005); and a distance, Rn, of the WD from the airborne stationbased on the determined longitude, latitude and RTT (Step 1007). In Step1009, the airborne station determines differences between earlier andlater determinations of the latitude and longitude and differences(ΔRTTs) between earlier and later determinations of RTT. In Step 1011,the airborne station scales the RTTs to account for horizontal distanceand altitude of the airborne station. In Step 1013, the airborne stationminimizing residuals between the determined ΔRTTs and a model ΔRTT, themodel ΔRTT being based at least in part on parameters α, v_(N), andv_(E) of the model, a being an angle between R_(n) and a reference axis,v_(N) being a velocity of the WD in a first direction and v_(E) being avelocity of the WD in a second direction perpendicular to the firstdirection. In Step 1015, the airborne station determines a location ofthe WD based at least in part on a value for a that minimizes theresiduals and based at least in part on the distance Rn.

In some embodiments, the model ΔRTT is based at least in part on:

${\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{Rn}} \right)^{2} + \left( \frac{d_{n - {q{perp}}}}{Rn} \right)^{2}} - 1} \right\}}$

-   -   where d_(n-q para)=COS(α) Δr_(N)+SIN(α) Δr_(E)+[COS(α) v_(N)        SIN(α) v_(E)]*(t_(n)−t_(n-q));    -   |d_(n-q perp)|=|−SIN(α) Δr_(N)+COS(α) Δr_(E)+[−SIN(α)        v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q))|; and Δr_(N) is a change in        latitude of the WD; Δr_(E) is a change in longitude of the WD        and C is a speed of light. In some embodiments, values of v_(N)        and v_(E) that minimize the residuals are used to predict an        average velocity v=√{square root over (v_(N) ²+v_(E) ²)} of WD        and a future location of the WD. In some embodiments, the WD        location is boxed by α±Δα, and by R±ΔR, where ΔR is related to        an uncertainty in short interface spacing (SIFS) time and where        a and Act are derived from a correlation matrix based on the        model. In some embodiments, the RTTs are scaled by a factor        given by

${F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}};$

where Alt_(n) is an altitude of the airborne station and R_(n) is therange in the same units as the altitude. In some embodiments, theresiduals are minimized based at least in part on minimizing a sum ofsquared residuals. In some embodiments, the process further includesscaling the longitude X_(n-q) by COS (Y_(n-q)). In some embodiments, ameasure of a final value of an RTT is based at least in part on anaverage of a number predetermined RTTs. In some embodiments, Rn isdetermined based at least in part on a delay that is determined when theWD is stationary. In some embodiments, the residuals are based at leastin part on a horizontal distance between the WD and the airbornestation.

As will be appreciated by one of skill in the art, the conceptsdescribed herein may be embodied as a method, data processing system,and/or computer program product. Accordingly, the concepts describedherein may take the form of an entirely hardware embodiment, an entirelysoftware embodiment or an embodiment combining software and hardwareaspects all generally referred to herein as a “circuit” or “module.”Furthermore, the disclosure may take the form of a computer programproduct on a tangible computer usable storage medium having computerprogram code embodied in the medium that can be executed by a computer.Any suitable tangible computer readable medium may be utilized includinghard disks, CD ROMs, optical storage devices, or magnetic storagedevices.

Some embodiments are described herein with reference to flowchartillustrations and/or block diagrams of methods, systems and computerprogram products. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable memory that can direct a computer or other programmable dataprocessing apparatus to function in a particular manner, such that theinstructions stored in the computer readable memory produce an articleof manufacture including instruction means which implement thefunction/act specified in the flowchart and/or block diagram block orblocks.

The computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

It is to be understood that the functions/acts noted in the blocks mayoccur out of the order noted in the operational illustrations. Forexample, two blocks shown in succession may in fact be executedsubstantially concurrently or the blocks may sometimes be executed inthe reverse order, depending upon the functionality/acts involved.Although some of the diagrams include arrows on communication paths toshow a primary direction of communication, it is to be understood thatcommunication may occur in the opposite direction to the depictedarrows.

Computer program code for carrying out operations of the conceptsdescribed herein may be written in an object oriented programminglanguage such as Java® or C++. However, the computer program code forcarrying out operations of the disclosure may also be written inconventional procedural programming languages, such as the “C”programming language. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer. In the latter scenario, theremote computer may be connected to the user's computer through a localarea network (LAN) or a wide area network (WAN), or the connection maybe made to an external computer (for example, through the Internet usingan Internet Service Provider).

While the above description contains many specifics, these should not beconstrued as limitations on the scope, but rather as an exemplificationof several embodiments thereof. Many other variants are possibleincluding, for examples: the details of the fitting process, the timespans used to gather data, the accepted errors used in the fittingprocess, the corrections for latitude and slope, the orbit or path ofthe airborne measuring station, the frequency of the transmission of theranging packets, the timing accuracy, and the type of packets used.Accordingly, the scope should be determined not by the embodimentsillustrated, but by the claims and their legal equivalents.

It will be appreciated by persons skilled in the art that the presentinvention is not limited to what has been particularly shown anddescribed herein above. In addition, unless mention was made above tothe contrary, it should be noted that all of the accompanying drawingsare not to scale. A variety of modifications and variations are possiblein light of the above teachings without departing from the scope of thefollowing claims.

1. A method in an airborne station for determining a location of amoving ground-based wireless device (WD), the method comprising: at eachof a plurality of positions of the airborne station, at times t_(n-q)for q=0 to q: determining the longitude X_(n-q) and latitude, Y_(n-q) ofthe airborne station; determining a round trip time RTT between theairborne station and the WD; determining a distance, Rn, of the WD fromthe airborne station based at least in part on the determined longitude,latitude and RTT; determining differences between earlier and laterdeterminations of the latitude and longitude and differences (ΔRTTs)between earlier and later determinations of RTT; scaling the RTTs toaccount for horizontal distance and altitude of the airborne station;minimizing residuals between the determined ΔRTTs and a model ΔRTT, themodel ΔRTT being based at least in part on parameters α, v_(N), andv_(E) of the model, a being an angle between Rn and a reference axis,v_(N) being a velocity of the WD in a first direction and v_(E) being avelocity of the WD in a second direction perpendicular to the firstdirection; and determining a location of the WD based at least in parton a value for α that minimizes the residuals and based at least in parton the distance Rn, the WD location being boxed by α±Δα, and by R±ΔR, ΔRbeing related to an uncertainty in short interface spacing (SIFS) timeand where α and Δα are derived from a correlation matrix based on themodel.
 2. The method of claim 1, wherein the model ΔRTT is based atleast in part on:${\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{Rn}} \right)^{2} + \left( \frac{d_{n - {q{perp}}}}{Rn} \right)^{2}} - 1} \right\}}$where d_(n-q para)=COS(α) Δr_(N)+SIN(α) Δr_(E)+[COS(α) v_(N)+SIN(α)v_(E)]*(t_(n)−t_(n-q)); |d_(n-q perp)|=|−SIN(α) Δr_(N)+COS(α)Δr_(E)+[−SIN(α) v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q))| Δr_(N) is a changein latitude of the WD; Δr_(E) is a change in longitude of the WD and Cis a speed of light.
 3. The method of claim 1, wherein values of v_(N)and v_(E) that minimize the residuals are used to predict an averagevelocity v=√{square root over (v_(N) ²+v_(E) ²)} of WD and a futurelocation of the WD.
 4. (canceled)
 5. The method of claim 1, wherein theRTTs are scaled by a factor given by${F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}};$ where Alt_(n) isan altitude of the airborne station.
 6. The method of claim 1, whereinthe residuals are minimized based at least in part on minimizing a sumof squared residuals.
 7. The method of claim 1, wherein a measure of afinal value of an RTT is based at least in part on an average of anumber predetermined RTTs.
 8. The method of claim 1, wherein Rn isdetermined based at least in part on a delay that is determined when theWD is stationary.
 9. The method of claim 1, wherein the residuals arebased at least in part on a horizontal distance between the WD and theairborne station.
 10. An airborne station for determining a location ofa moving ground-based wireless device (WD), the airborne stationcomprising processing circuitry configured to: at each of a plurality ofpositions of the airborne station, at times t_(n-q) for q=0 to q:determine the longitude X_(n-q) and latitude, Y_(n-q) of the airbornestation; determine a round trip time RTT between the airborne stationand the WD; determine a distance, Rn, of the WD from the airbornestation based at least in part on the determined longitude, latitude andRTT; determine differences between earlier and later determinations ofthe latitude and longitude and differences (ΔRTTs) between earlier andlater determinations of RTT; scale the RTTs to account for horizontaldistance and altitude of the airborne station; minimize residualsbetween the determined ΔRTTs and a model ΔRTT, the model ΔRTT beingbased at least in part on parameters α, v_(N), and v_(E) of the model, abeing an angle between Rn and a reference axis, v_(N) being a velocityof the WD in a first direction and v_(E) being a velocity of the WD in asecond direction perpendicular to the first direction; and determine alocation of the WD based at least in part on a value for a thatminimizes the residuals and based at least in part on the distance Rn,the WD location being boxed by α±Δα, and by R±ΔR, ΔR being related to anuncertainty in short interface spacing (SIFS) time and where α and Δαare derived from a correlation matrix based on the model.
 11. Theairborne station of claim 10, wherein the model ΔRTT is based at leastin part on:${\Delta{RTT}} = {\left( \frac{2R_{n}}{C} \right)\left\{ {\sqrt{\left( {1 + \frac{d_{n - {q{para}}}}{Rn}} \right)^{2} + \left( \frac{d_{n - {q{perp}}}}{Rn} \right)^{2}} - 1} \right\}}$where d_(n-q para)=COS(α) Δr_(N)+SIN(α) Δr_(E)+[COS(α) v_(N)+SIN(α)v_(E)]*(t_(n)−t_(n-q)); |d_(n-q perp)|=|−SIN(α) Δr_(N)+COS(α)Δr_(E)+[−SIN(α) v_(N)+COS(α) v_(E)]*(t_(n)−t_(n-q))| Δr_(N) is a changein latitude of the WD; Δr_(E) is a change in longitude of the WD and Cis a speed of light.
 12. The airborne station of claim 10, whereinvalues of v_(N) and v_(E) that minimize the residuals are used topredict an average velocity v=√{square root over (v_(N) ²+v_(E) ²)} ofWD and a future location of the WD.
 13. (canceled)
 14. The airbornestation of claim 10, wherein the RTTs are scaled by a factor given by${F = \frac{\sqrt{R_{n}^{2} - {Alt}_{n}^{2}}}{R_{n}}};$ where Alt_(n) isan altitude of the airborne station.
 15. The airborne station of claim10, wherein the residuals are minimized based at least in part onminimizing a sum of squared residuals.
 16. The airborne station of claim10, wherein a measure of a final value of an RTT is based at least inpart on an average of a number predetermined RTTs.
 17. The airbornestation of claim 10, wherein Rn is determined based at least in part ona delay that is determined when the WD is stationary.
 18. The airbornestation of claim 10, wherein the residuals are based at least in part ona horizontal distance between the WD and the airborne station.